When scaling up an image in a longitudinal direction, or converting an interlaced image into a progressive image, it is necessary to define an image Fin that has alternating lines, one having pixel values in a vertical direction and the other having no pixel value as given by EQ. (1), and interpolate Null's based on information on the lines having pixel values:
                    [                  Equation          ⁢                                          ⁢          1                ]                                                                      Fin          ⁡                      (                          x              ,              y                        )                          =                  {                                                                                                                F                      ⁡                                              (                                                  x                          ,                          y                                                )                                                                                                                        if                      ⁢                                                                                          ⁢                                              (                                                                              y                            ⁢                                                                                                                  ⁢                                                          mod                              ⁢                              2                                                                                =                          0                                                )                                                                                                                                  Null                                                        else                                                              ⁢                                                          ⁢              or              ⁢                                                          ⁢                              Fin                ⁡                                  (                                      x                    ,                    y                                    )                                                      =                          {                                                                                          F                      ⁡                                              (                                                  x                          ,                          y                                                )                                                                                                                        if                      ⁡                                              (                                                                              y                            ⁢                                                                                                                  ⁢                            mod                            ⁢                                                                                                                  ⁢                            2                                                    =                          1                                                )                                                                                                                                  Null                                                        else                                                                                                          EQ        .                                  ⁢                  (          1          )                    where Fin(x, y) designates a value of Fin at coordinates (x, y).
One conventional interpolation method is an edge-adaptive interpolation method (Non-patent Document 1, Patent Document 1). The edge-adaptive interpolation method involves selecting a combination of pixels having a highest similarity from pairs of pixels on upper and lower lines that are point-symmetrical with respect to an interpolated pixel (x, y) and using the combination in interpolation, which can excellently reproduce oblique lines.
Now the conventional edge-adaptive interpolation method will be described with reference to FIG. 20. FIG. 20 is a block diagram showing a configuration of an image scaling-up apparatus using the conventional edge-adaptive interpolation method. The image scaling-up apparatus using the edge-adaptive interpolation method shown in FIG. 20 comprises optimally used pixel searching means 11 and interpolating means 12, and is supplied with an image Fin and a searched range as input and outputs an interpolated image.
The optimally used pixel searching means ills supplied with the image Fin and searched range as input, selects a pair of pixels having a highest similarity from pairs of pixels on upper and lower lines point-symmetric with respect to an interpolated pixel within the searched range (−φ−φ) for each interpolated pixel, and outputs optimally used pixel information indicating the positional relationship between the interpolated pixel and selected pair. FIG. 17 shows an explanatory diagram representing the summary of the processing at the optimally used pixel searching means 11. In the explanatory diagram of FIG. 17, an example of a searched range with φ=2 is used. First, (2φ+1) pairs of pixels point-symmetric with respect to an interpolated pixel are selected from a region delimited by a searched range specified for upper and lower lines of an interpolated pixel. The symbol ‘p’ in the drawing is a value representing a positional relationship between the interpolated pixel and a pixel pair. From the pixel pairs, one having a highest similarity is defined as optimally used pixels, and the value of ‘p’ for the selected pixel pair is output as optimally used pixel information ‘k’ Selection of a pair having a high similarity is implemented by a method of selecting a pixel pair that minimizes an evaluation function C1(p) of EQ. (2) or a method of selecting a pixel pair that minimizes an evaluation function C2(p) of EQ. (3). In Patent Document 2, the similarity is synthetically determined from a plurality of evaluation functions such as those of EQs. (2) and (3).
                    [                  Equation          ⁢                                          ⁢          2                ]                                                                      C          ⁢                                          ⁢          1          ⁢                      (            p            )                          =                                                      Fin              ⁡                              (                                                      x                    +                    p                                    ,                                      y                    -                    1                                                  )                                      -                          Fin              ⁡                              (                                                      x                    -                    p                                    ,                                      y                    +                    1                                                  )                                                                                  EQ        .                                  ⁢                  (          2          )                                        [                  Equation          ⁢                                          ⁢          3                ]                                                                      C          ⁢                                          ⁢          2          ⁢                      (            p            )                          =                              ∑                          q              =                              -                1                                      1                    ⁢                                                                                                                            Fin                      ⁢                                              (                                                                              x                            +                            p                            +                            q                                                    ,                                                      y                            -                            1                                                                          )                                                              -                                                                                                                    Fin                    ⁡                                          (                                                                        x                          -                          p                          +                          q                                                ,                                                  y                          +                          1                                                                    )                                                                                                                                          EQ        .                                  ⁢                  (          3          )                    
The interpolating means 12 is supplied with the image Fin and optimally used pixel information as input, and outputs an interpolated image. An output pixel value FI(x, y, t) for an interpolated pixel (x, y) at coordinates (x, y) is calculated using optimally used pixel information k(x, y) at the interpolated pixel according to EQ. (4).
                    [                  Equation          ⁢                                          ⁢          4                ]                                                                      FI          ⁡                      (                          x              ,              y              ,              t                        )                          =                                                                                                  Fin                    ⁢                                          (                                                                        x                          +                                                      k                            ⁡                                                          (                                                              x                                ,                                y                                                            )                                                                                                      ,                                                  y                          -                          1                                                                    )                                                        +                                                                                                      Fin                  ⁡                                      (                                                                  x                        -                                                  k                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                                              ,                                              y                        +                        1                                                              )                                                                                2                                    EQ        .                                  ⁢                  (          4          )                    
Patent Document 1: JP-P1992-355581A
Patent Document 2: JP-P2005-293361A
Non-patent Document 1: “Deinterlacing—an overview,” De Haan, G., Beliefs, E. B, Proceedings of the IEEE, Vol. 86, Issue 9, September 1998, pp. 1839-1857